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证明了方法的局部收敛性和局部超线性收敛性。Local convergence and local superlinear convergence rate are proved.

本文还讨论了特殊情况下算法的超线性收敛性。The superlinear convergence for some special cases is also discussed.

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并在通常条件下证明了方法的全局收敛性。The authors also prove that the method has superlinear convergence rate.

作为结果，算法具有全局和超线性收敛性。As a result, the proposed algorithm has global and superlinear convergence.

另外在较弱的条件下，证明该方法具有超线性收敛性。We also prove that the method has superlinear convergence rate under some mild conditions.

并将抽象结果应用到超线性微分方程两点边值问题。Finally, the abstract results are applied to superlinear two-point boundary value problems.

此外，我们在较弱的生长条件下证明了算法2．1的超线性收敛率。Furthmore, we prove the superlinear convergence of Algorithm 2.1 under mild growth condition.

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在适当的假设条件下，我们证明了算法具有全局收敛性和超线性收敛性。Under mild conditions, we establish the global and superlinear convergence results for the method.

在适当的条件下我们将证明此方法的全局收敛性和超线性收敛性。We prove that the method possesses the global and superlinear convergence under suitable conditions.

在适当的条件下，证明了算法的全局收敛性及超线性收敛性。The global convergence and superlinear convergence results of algorithm are preserved under suitable conditions.

证明该算法在目标函数为一致凸时具有局部超线性收敛性。It was proved that, when the objective function was uniformly convex, this algorithm possessed superlinear convergence.

使用只有一个上解或下解的条件，证明了一类超线性算子不动点的几个结果。By using fixed point index, we prove some existence results of positive fixed points of a class of superlinear operator.

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在合理的假设条件下，证明了算法的整体收敛性与局部超线性收敛速率。Global convergence and local superlinear convergence rate of the proposed algorithm are established on some reasonable conditions.

由于引进了新的逼近技术，该方法具有全局收敛性和局部超线性收敛性。The global convergence and local superlinear convergence of the method are established by introducing new approximation techniques.

通过不动点指数理论，讨论了一类超线性算子方程的多重解问题。By fixed point index theory, multiplicity question of solutions to superlinear operator equations in ordered Banach space is discussed.

研究偶数阶常微分方程的边值问题，在其非线性项具有超线性增长性时，给出其解存在的充分条件。Investigates even order superlinear boundary value problems are investigated. Sufficient conditions for existence of solutions are obtained.

该算法无需计算拉格朗日函数的海色矩阵，并且在适当的假设下，算法具有全局和局部超线性收敛性。Under suitable assumptions we prove that the new algorithm is not only globally convergent, it also has a local superlinear convergence rate.

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考虑一类非线性项具有超线性增长的半线性椭圆型障碍问题的多解性。Consider the existence of the multiple solutions of some semilinear elliptic obstacle problem provided that the nonlinear term is superlinear.

在这篇文章中，我们得到了非线性函数在无穷远处超线性增长时一类高维半线性双曲方程的整体精确能控性。In this paper, we obtain the global exact controllability for a class of multidimensional semilinear hyperbolic equations with a superlinear nonlinearity.

本文利用不动点指数理论研究了一类非线性算子特征元的全局结构，证明了解集存在无界连通分支并给出了多个正解的存在性结果。In this paper, we investigate some global characteristics of the eigenvectors of a class of superlinear operators by means of the fixed point index theory.